ใบความรู้ที่ 1.2 รากที่ n...
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Transcript of ใบความรู้ที่ 1.2 รากที่ n...
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1.2 n
(32201) 1
1.2 n
x, y y x y2 = x
1 1. 42 = 16 4 16 2. (-4)2 = 16 -4 ......................................... 3. 24 = 16 2 ............................................. 4. (-2)4 = 16 ............... ............................................. 5. 33 = 27 ................. ................................................ 6. (-3)3 = -27 ............... ............................................... 7. 25 = 32 ............. ............................................... 8. (-2)5 = -32 ............... ...............................................
1. a n n a 2 16 4 -4 42 = 16 (-4)2 = 16 2. a n n a 1 8 2 23 = 8 -27 -3 (-3)3 = -27 3. a n n a -9 -9 4. a n n a 1 -27 -3 (-3)3 = -27 n a n a
n a n a n a
n a n a 1. a > 0 ; n a n a 9 > 0 9 9
9 = 3 9 8 > 0 3 8 8 3 8 = 2 8
16 16 -2, 16 3, , 27 -3, , -27 2, , 32 -2, , -32
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2. a < 0 n ; n a n a -32 < 0 5 32 -32 5 32 = -2 -32
3. a = 0 n a = 0 n 0 0 2 81 3 4 81 = 3
-125 -5 3 125 = -5
(1) n a n a n a
n 3 3 (2) n = 2 2 (3) n 1 = 1
a n n na = a n
n na = a n 3
1. 4 16 = 4 42 = 2 = 2 ( n = 4 ) 2. 2)3( = 3 = 3 ( n = 2 ) 3. 5 32 = 5 5)2( =-2 ( n = 5 )
n n, m 1 a, b n a n b
1. nn a)( = a 2. nn ba = n ab
3. n
n
b
a = nb
a b 0 n a 0 b > 0
4. m n a = nm a 5. nm ma = n a n a 0
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4 (1) 2425 = 2)45( = 29
(2) 3638 = 3)68( = 32 (3) 525453 = 5)243( = 55 (4) 77379 = 7)139( = 75 5 32283 = 2162)243
= 242)22(3 = 24226 = 2)416( = 29 6 333 2419281 = 333 38364327
= 333 323433 = 3 3)243( = 3 35
7 33327
32818243 =
3
333
27
323278383
= 333 33
2)33(8)32(3
= 333 33
232436
= 3 3)3
2246(
= 3 33
56
n 8 3263 3263 = )36)(23( = 186 = 296 = 2)36( = 218
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9 )27584(33 )27584(33 = )27584(33 = 3953324433 = )33)(353()23)(243( = 345624 = 135624
10 )3222)(335( )3222)(335( = )32)(3()22)(3()32)(35()22)(35( = 66220610 = 6814
11 3 96 3 96 = 23 232 3 96 = 6 46 33 332 = 6 433 332 = 6 73 32 = 6 66 3 332 = 66 3 332 = 6 243
12 (1) 5
80 =
580
= 16 = 4
(2) 3523 =
335323
=
335323
=
3563
= 56
13 3
3
185
3
3
185
= 3 2
3
325
= 3 23 2
3 23
2332235
= 3 33
3
32125
= 6603
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yx 2 yx 2 2ba a0 b0
2ba = bbaa 2 = abba 2)( x = a + b y = ab yx 2 = abba 2)(
yx 2 = 2ba (1) 2 yx 2 = 2 2ba = ba )( ba (2) 2 yx 2 = 2 2ba = ba )( ba 2 yx 2
1. a 0, b 0 x = a + b y = ab 2 yx 2 = ba )( ba
2 yx 2 = ba )( ba 14 2 55216 x = 16 = 11 + 5 y = 55 = 115 2 55216 = 511 )511( 15 2 24211
x = 11 = 8 + 3 y = 24 = 83 2 24211 = 38 )38( 16 2 5818 5818 yx 2 5818 = 54218 = 54218 2 = 80218 x = 18 = 10 + 8 y = 80 = 108 2 5818 = 2 80218
= 810 )810(
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17 2 154 154 yx 2
154 = 152
24
= 22
1524
= 4
1524
x = 4 = 2
3
2
5 y =
415 =
2
3
2
5
2 154 = 2 4
1524
=2
3
2
5 )
2
3
2
5(
=2
3
2
5
2
3
2
5
